Can paxil (paroxetine) 25mg cause constipation?

Unlikely: More likely that it causes diarrhea.

Yes: Many antidepressants can cause constipation, and unless something else has changed at the same time that you started the paxil, (paroxetine) it might be the cause. We recommend increasing fluid intake, dietary fiber intake (fresh fruits, vegetables, whole grain products); and if that's not enough, a fiber supplement and stool softener, laxatives should be a last resort.

Paxil: See: https://www.drugs.com/sfx/paxil-side-effects.html Paxil can cause either constipation or diarrhea in over 10% of people taking it.